Fungrim entry: a6667d

{\sin}^{(r + 2)}(z) = -{\sin}^{(r)}(z)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}

TeX:

{\sin}^{(r + 2)}(z) = -{\sin}^{(r)}(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`Sin`	$\sin(z)$	Sine
`CC`	$\mathbb{C}$	Complex numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("a6667d"),
    Formula(Equal(ComplexDerivative(Sin(z), For(z, z, Add(r, 2))), Neg(ComplexDerivative(Sin(z), For(z, z, r))))),
    Variables(z, r),
    Assumptions(And(Element(z, CC), Element(r, ZZGreaterEqual(0)))))

Topics using this entry

Sine

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC